As far as action type, I am simply bolt action trash. I have used bolt actions forever, and that is my choice.
Simply thinking of speed, a semi auto would be hands down the fastest, then a pump IMO. My Dad has used a Remington 760 in 270 Win since about 1970, his only big game rifle. I have seen/heard him work the action so fast on running critters that you would have thought it was a semi auto. I grew up shooting pump shotguns and can run rounds through pretty dang fast.
As far as lever actions, they have never grabbed a hold of me. Have had a few, BLR, Marlins, Winchesters. 22LR to 45-70. There is no way I could ever take one on an "important" hunt. I would certainly take a pump action if needed.
If not a bolt action, hand me a Rem 760/7600 in 30-06 or 35 Whelen and I am sure I could not only kill a bear, but be ready for follow up shots post haste,
